88 Cadillac Allante and Shaking

I looked at an 88 Allante today with 92K miles. The car rode and drove well, but there was a strong shaking (almost like a miss) when the car accelerated from stop and also when it slowed from city/highway speed to a stop. The shaking was not so noticeable while idling (stopped). I did not notice and smoking from the car, and other than the shaking, the car performed well. Any ideas on what the problem could be?

Tires, Wheels, Worn Suspension/Steering Components, Transmission/Drive Train, Engine Problems, Whatever ?

It’s probably nothing that either a little or a lot of money couldn’t fix. If I were considering buying a car like this, the shaking would be a deal breaker pending either a pre-sale repair or at least a firm mechanic’s inspection and diagnosis.

I don’t know anything about horses, but I wouldn’t buy one that limps or coughs.